ShodhPatra: International Journal of Science and Humanities

Exploration of Divergent Translations and Algebraic Characteristics of Intuitionistic Fuzzy Ideals in Diverse Algebraic Systems

This study investigates the complex landscape of intuitionistic fuzzy ideals (IFIs) within a variety of algebraic structures, focusing on their divergent translations and associated algebraic properties. Intuitionistic fuzzy sets, which extend classical fuzzy sets by incorporating degrees of both membership and non-membership, provide a robust framework for modeling uncertainty. Their application in abstract algebra gives rise to intuitionistic fuzzy ideals—generalized forms of classical ideals—that enhance reasoning in uncertain environments. The research analyzes how IFIs behave under convolutional fuzzy translation in BCK/BCI-algebras and explores anti-intuitionistic fuzzy ideals using level-set based translations. Additionally, it introduces Cartesian product operations over opposite IF α-translations within division HA-algebras, offering new structural interpretations. The study draws upon advanced decision-making models and distance measures from fuzzy set theory to substantiate its theoretical findings with practical implications. By bridging intuitionistic fuzzy logic with abstract algebra, the paper contributes to a deeper understanding of uncertainty modeling, laying the groundwork for innovations in mathematics, decision sciences, engineering and computer applications.